Question

PLEASE HELP!!!!!!

The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h=-30cos(2pi/5 t). At which times will the spring be at a height of 20 in. above equilibrium?

Answer Options:

1.3 seconds
1.8 seconds
3.2 seconds
4.3 seconds
5.7 seconds

THERE ARE 2 CORRECT ANSWERS!!!

Answer 1

Answer: the answers are 1.8 and 3.2 seconds. So both B and C.

Explanation:

Answer 2

Option 1 and 3 - 1.3 seconds and 3.2 seconds

Explanation:

Given : The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is
`h=-30\cos((2\pi)/(5) t)`.

To find : At which times will the spring be at a height of 20 in. above equilibrium?

Solution :

We have given,

The equation that models the height above or below equilibrium in inches

`h=-30\cos((2\pi)/(5) t)`

We have to find at h=20 inches the time of spring.

We show it graphically,

Plot the graph of the model
`h=-30\cos((2\pi)/(5) t)`

Then, Substitute h=20

The points of their intersections are the solution of the model.

The intersection points are (1.831,20), (3.169,20) and many more.

From the given options,

The time are 1.3 seconds and 3.2 seconds.

Therefore, Option 1 and 3 are correct.

Refer the attached figure below.